The utility of the classical Karhunen‐Loève expansion of a second order process is limited to
its practical derivation, because it depends upon the solution of a Fredholm integral …

Using functional integral methods, the Laplace transform of the square of the Ornstein-
Uhlenbeck process X(t) integrated over 0\leqqt\leqqT is calculated. Via the complex …

Differentiation of the modified approximative Karhunen–Loève expansion of a stochastic
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We derive the explicit formula for the joint Laplace transform of the Wishart process and its
time integral, which extends the original approach of Bru (1991). We compare our …

A simulation procedure for obtaining discretely observed values of Ornstein–Uhlenbeck
processes with given (self-decomposable) marginal distribution is provided. The method …

In this paper we deal with the Wiener–Hermite expansion of a process generated by an Itô
stochastic differential equation. The so-called Wiener kernels which appear in the functional …

This paper nds the eigenvalues and eigenvectors of the covariance matrix associated with
multi-dimensional Brownian motion and the Ornstein-Uhlenbeck processes. The result is …

The generalised Ornstein–Uhlenbeck process constructed from a bivariate Lévy process (ξt,
ηt) t⩾ 0 is defined aswhere V0 is an independent starting random variable. The stationarity …

In this article we propose a maximum likelihood methodology to estimate the parameters of
a one-dimensional stationary process of Ornstein-Uhlenbeck type that is constructed via a …

In this paper we present a class of continuous-time processes arising from the solution of the
generalized Langevin equation and show some of its properties. We define the theoretical …